He said lawmakers will meet with the president again after Thanksgiving.

Rep. Nancy Pelosi, the top Democrat in the House, said she "feel confident that a solution may be in sight."

White House Press Secretary Jay Carney said Obama and the legislative leaders "agreed to do everything possible to find a solution." Carney said White House officials will continue the talks as Obama travels to Asia. Obama leaves on Saturday for a trip that will include a historic stop in Myanmar.

After the meeting, Boehner and Senate Minority Leader Mitch McConnell said they offered higher tax revenue as part of a deal. Boehner said he outlined a framework that is consistent with Obama's call for a "balanced" approach of both higher revenue and spending cuts.

"To show our seriousness, we put revenue on the table, as long as it's accompanied by serious spending cuts," Boehner said.

In offering conditional backing for new revenue, McConnell said reforms to social safety net programs also are necessary.

"We fully understand that you can't save the country until you have entitlement programs that fit the demographics of changing America in the coming years," the Senate minority leader said. "We're prepared to put revenue on the table provided we fix the real problems."

The meeting marked the first time Obama, a Democrat, sat down with his Republican opposition since he won re-election last week.

All eyes were on Boehner, who will have to balance the wishes of a newly confident president with the demands of his rank-and-file conservatives.

The hour-long talks began with Obama calling for "tough compromises."

Obama Meets With Congressional Leaders

President Obama meets with Congressional leaders to discuss the fiscal cliff. He also takes time to wish House Speaker John Boehner a happy birthday.

"My hope is that this is going to be the beginning of a fruitful process where we are able to come to an agreement that will reduce our deficit in a balanced way, that we will deal with some of these long-term impediments to growth, and we're also going to be focusing on making sure that middle class families are able to get ahead," Obama said, sitting next to Boehner.

"Our challenge is to make sure that, you know, we are able to cooperate together, work together, find some common ground, make some tough compromises, build some consensus to do the people's business," he said.

The session was not expected to yield much in the way of tangible results, but it could create a template for the coming weeks of negotiations. And it began on a jovial note. Obama noted that the talks were being conducted a day before Boehner's birthday.

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"We're not going to embarrass him with a cake, because we didn't know how many candles were needed," Obama said. Boehner is turning 63.

And after the meeting, Reid said: "We have the cornerstone of being about to work something out."

Market futures had indicated a higher open Friday after The Wall Street Journal reported White House officials were in discussions that could indicate increased flexibility in negotiations with Republicans. (Read More: White House in Talks to Replace Sequester: Report.)

Citing sources familiar with the matter, the Journal said officials were in advanced, internal talks to replace spending cuts set to begin in January with a separate package of spending cuts and tax increases. The White House had no comment on the report.

Business leaders say uncertainty about the crisis is already weighing on the economy as employers postpone hiring and capital expenditures until they get a better sense of the tax and spending environment.

Investors worry that if no deal is reached on the large, automatic budget cuts and tax hikes set to begin next year, the economy could slip into recession.

"This is the first time we've had one iota of anything constructive being done,'' said Todd Schoenberger, managing principal at the BlackBay Group in New York. "That's very positive, but you can be flexible and still have us go over the cliff. Wall Street traders remain very nervous and need something concrete to get done.''

Both sides are pledging cooperation even as they dig in on their long-held opening positions, and are eager to reassure nervous investors that they will reach a deal.

House Leadership on Fiscal Cliff Discussions

Rep. Peter Roskam, (R-IL), recaps what went on between Congressional leaders and President Obama.

"Going over the fiscal cliff, in my view, is a bucket of crazy,'' Republican Rep. Peter Roskam, one of Boehner's deputies, said at a budget conference.